Semi-Lagrangian Advection Methods and Their Applications in Geoscience

Semi-Lagrangian Advection Methods and Their Applications in Geoscience provides a much-needed resource on semi-Lagrangian theory, methods, and applications. Covering a variety of applications, the book brings together developments of the semi-Lagrangian in one place and offers a comparison of semi-Lagrangian methods with Eulerian-based approaches. It also includes a chapter dedicated to difficulties of dealing with the adjoint of semi-Lagrangian methods and illustrates the behavior of different schemes for different applications. This allows for a better understanding of which schemes are most efficient, stable, consistent, and likely to introduce the minimum model error into a given problem.

Beneficial for students learning about numerical approximations to advection, researchers applying these techniques to geoscientific modeling, and practitioners looking for the best approach for modeling, Semi-Lagrangian Advection Methods and Their Applications in Geoscience fills a crucial gap in numerical modeling and data assimilation in geoscience.

Provides a single resource for understanding semi-Lagrangian methods and what is involved in its applicationIncludes exercises and codes to supplement learning and create opportunities for practiceIncludes coverage of adjoints, examining the advantages and disadvantages of different approaches in multiple coordinate systems and different discretizationsIncludes links to numerical datasets and animations to further enhance understanding

1. Introduction 2. Eulerian modeling of advection problems 3. Stability, consistency, and convergence of Eulerian advection based numerical methods 4. History of semi-Lagrangian methods 5. Semi-Lagrangian methods for linear advection problems 6. Interpolation methods 7. Stability and consistency analysis of semi-Lagrangian methods for the linear problem 8. Advection with nonconstant velocities 9. Nonzero forcings 10. Semi-Lagrangian methods for two-dimensional problems 11. Semi-Lagrangian methods for three-dimentional problems 12. Semi-Lagrangian methods on a sphere 13. Shape-preserving and mass-conserving semi-Lagrangian approaches 14. Tangent linear modeling and adjoints of semi-Lagrangian methods 15. Applications of semi-Lagrangian methods in the geosciences